The invention relates to active acoustic attenuation systems operating in a waveguide where an acoustic wave propagates longitudinally through the waveguide and has plane wave mode and higher order mode transverse modal energy. In particular, the invention relates to a system where the various modes are decoupled before the acoustic system is modeled in an adaptive filter model.
The invention arose during continuing development efforts relating to active acoustic attenuation systems, including the subject matter shown and described in U.S. Pat. Nos. 4,677,676; 4,815,139; 4,837,834; 4,987,598; 5,022,082, 5,216,721; and 5,216,722, all of which are assigned to the assignee of the present invention and are incorporated herein by reference.
At low frequencies, sound propagates down a duct as a series of plane waves. Above a critical "cut-on" frequency, however, sound can propagate in the plane wave mode plus one or more higher order modes. Each higher order mode has a cut-on frequency. The cut-on frequency for each higher order mode depends on the velocity of sound through the duct and the duct geometry. Above the cut-on frequency for a specific mode, the wave mode is stable and propagates without attenuation. Below the cut-on frequency, the mode decays exponentially as it propagates down the duct after it has been excited. Commercial air duct systems typically have a large enough cross section to support one or more higher order modes in the frequency range of interest for active noise control.
In general, active acoustic attenuation systems inject a canceling acoustic wave to destructively interfere with and cancel an input acoustic wave. Referring to FIGS. 1 and 3, it is typical to sense the input acoustic wave with an input microphone and the output acoustic wave with an error microphone. The input microphone supplies an input or feedforward signal to an electronic controller, and the error microphone supplies an error or feedback signal to the electronic controller. The electronic controller, in turn, supplies a correction signal to a canceling loudspeaker, which injects a canceling acoustic wave to destructively interfere with the input acoustic wave, such that the output acoustic wave at the error microphone is zero (or at least reduced). If a sound wave propagating down the duct is a plane wave having uniform pressure across the duct, the location across the duct of the microphone and the canceling loudspeaker does not matter. However, if the acoustic spectrum extends above the first higher order mode cut-on frequency, there may be energy in several modes. In this case, a single channel or single-input-single-output (SISO) system as shown in FIGS, 1 and 3 gives poor cancellation above the modal cut-on frequency and may even add acoustic power or become unstable.
The modal distribution of acoustic energy can become complicated. Referring to FIG. 8, an instantaneous pressure distribution in a cross sectional plane normal to the longitudinal axis of a rectangular duct is shown for each of several modes. The symbols "+" and "-" denote regions of positive and negative instantaneous pressure. Separating these regions are planes of zero pressure called nodal planes. The pressure will vary sinusoidally in time in the "+" and "-" regions, but will always be zero on the nodal planes.
As shown in FIG. 8, the pressure distribution across a duct can become complicated inasmuch as nodal planes associated with higher order modes can occur along both horizontal planes (designated as n) and vertical planes (designated as m). As explained by Eriksson, "Higher Order Mode Effects In Circular Ducts and Expansion Chambers", J. Acoust. Soc. Am. 68(2), August 1980, the cut-on frequency, f.sub.c, in Hertz, for each (m,n) mode in a rectangular duct is given by: ##EQU1## where c is the velocity of sound in meters/second, a and b are the lengths of the sides of the duct in meters, and m and n are integers 0,1,2, . . . . In the above-cited paper, Eriksson also discloses a similar analysis for circular ducts. It can be appreciated from Equation (1) and FIG. 8 that the modal distribution of acoustic energy can become complicated when multiple modes are propagating.
A single-input-single-output (SISO) system cancels the plane wave mode. Multiple-input-multiple-output (MIMO) systems have been developed, and improve attenuation of multiple modes. Examples of MIMO systems are the systems disclosed in U.S. Pat. Nos. 4,815,319, 5,216,721, and 5,216,722.
An adaptive 2-x-2 MIMO controller with infinite impulse response (IIR) filters as described in the above referenced U.S. Pat. No. 5,216,721 to Melton is shown in FIG. 12. The 2-x-2 MIMO controller shown in FIG. 12 requires about four times the computational power as the SISO controller shown in FIGS. 1 and 3. In addition, a like amount of computational power is required to model error or feedback signals in the same manner.
A 3-x-3 MIMO controller demanding 9 times the computational power of a SISO controller is required to control an input disturbance consisting of a plane wave plus the first two higher order modes. In general, controlling n modes requires an n-x-n MIMO controller, which demands n.sup.2 times the computational resources of a SISO controller. Although it is possible in the prior art to use a system that does not require n.sup.2 times the computing power of a SISO controller, such a system will not in all circumstances completely characterize the input disturbance. The result will be poor attenuation, unwanted addition of acoustic energy or instability. This is especially true when the range of frequency of the input disturbance is broad and the acoustic profile becomes distorted quickly as the disturbance travels down the duct.